# rpf.grm: Create a graded response model In rpf: Response Probability Functions

## Description

For outcomes k in 0 to K, slope vector a, intercept vector c, and latent ability vector theta, the response probability function is

P(pick=0|a,c,th) = 1-P(pick=1|a,c_1,th)

P(pick=k|a,c,th) = 1/(1+exp(-(a th + c_k))) - 1/(1+exp(-(a th + c_(k+1))))

P(pick=K|a,c,th) = 1/(1+exp(-(a th + c_K)))

## Usage

 `1` ```rpf.grm(outcomes = 2, factors = 1, multidimensional = TRUE) ```

## Arguments

 `outcomes` The number of choices available `factors` the number of factors `multidimensional` whether to use a multidimensional model. Defaults to `TRUE`.

## Details

The graded response model was designed for a item with a series of dependent parts where a higher score implies that easier parts of the item were surmounted. If there is any chance your polytomous item has independent parts then consider `rpf.nrm`. If your categories cannot cross then the graded response model provides a little more information than the nominal model. Stronger a priori assumptions offer provide more power at the cost of flexibility.

## Value

an item model

Other response model: `rpf.drm()`, `rpf.gpcmp()`, `rpf.grmp()`, `rpf.lmp()`, `rpf.mcm()`, `rpf.nrm()`
 ```1 2``` ```spec <- rpf.grm() rpf.prob(spec, rpf.rparam(spec), 0) ```